Locate the packing nut that is right behind the handle. Grab the faucet body with a pair of pliers and turn the packing nut clockwise with a wrench. Sometimes the packing nut only needs a small adjustment like this to stop the drip.
Shut off the water supply to the faucet. Go under the house and locate the shutoff valve on the line going to the faucet. Turn the shutoff valve clockwise to turn off the water supply, if you have a round valve handle. If you have a lever shutoff valve, turn the valve lever 90 degrees to shut off the water.
Go back to the outside faucet and turn the faucet handle all the way to the full open position. Grab the faucet body with the pliers and turn the nut between the packing nut and the spout counterclockwise with a wrench. This is the valve body nut that secures the valve to the faucet body. Once the assembly is loose, unthread it by hand and pull the assembly out of the faucet body.
Remove the screw securing the faucet handle to the assembly with a Phillips-head screwdriver. Pull the handle off the assembly. Hold the valve nut with a wrench and turn the packing nut counterclockwise to disconnect the packing nut from the valve body nut. Slide the packing nut off the stem.
Pull out the washer in the bottom of the packing nut. Locate the screw that secures the compression washer on the end of the valve stem. Remove the screw with a Phillips-head screwdriver and pull off the compression washer.
Take the washers to a hardware store to purchase replacements. You want washers that match the current ones for size and thickness.
Place the new compression washer over the end of the valve stem and secure with the retaining screw. Insert the packing nut washer into the packing nut. Slide the packing nut over the outer stem with the threads pointing to the valve body nut. Thread the packing nut to the valve body nut and tighten with a wrench.
Position the faucet handle over the outer stem and secure with the retaining screw. Insert the valve body back into the faucet body. Tighten the valve body nut to the faucet body with a wrench. Hold the faucet body with a pair of pliers when tightening the valve body nut. Go under the house and turn on the water supply to the faucet.